Grade 6 Geometry Worksheet: Area of Triangles, Parallelograms & Trapezoids

Let's solve each problem on the "Area of triangles, parallelograms & trapezoids" worksheet step by step. We’ll use the appropriate formulas for each shape.

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🔷 Formulas:

1. Triangle:
$$
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
$$

2. Parallelogram:
$$
\text{Area} = \text{base} \times \text{height}
$$

3. Trapezoid:
$$
\text{Area} = \frac{1}{2} \times (\text{base}_1 + \text{base}_2) \times \text{height}
$$

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Now let’s go through each figure:

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1. Triangle

- Base = 14
- Height = 5.25 (this is the perpendicular height from the base)
- Side lengths: 13 and 5 are just side lengths — not needed unless we're using Heron’s formula, but here we have a height given.

$$
\text{Area} = \frac{1}{2} \times 14 \times 5.25 = 7 \times 5.25 = 36.75
$$

✔ Answer: 36.75 square units

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2. Parallelogram

- Base = 6
- Height = 3 (the vertical side labeled 3 is the height, since it’s perpendicular to the base)
- The other side (5.63) is slanted — not used directly

$$
\text{Area} = \text{base} \times \text{height} = 6 \times 3 = 18
$$

✔ Answer: 18 square units

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3. Parallelogram

- Base = 5
- Height = 2 (vertical side labeled 2 is the height)
- 3.01 is the slant side — not needed

$$
\text{Area} = 5 \times 2 = 10
$$

✔ Answer: 10 square units

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4. Trapezoid

- Bases: 5 and 4.65
- Height = 2 (the perpendicular distance between the two bases)

$$
\text{Area} = \frac{1}{2} \times (5 + 4.65) \times 2 = \frac{1}{2} \times 9.65 \times 2 = 9.65
$$

✔ Answer: 9.65 square units

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5. Trapezoid

- Bases: 6 and 13
- Height = 3.30 (the perpendicular segment between the two bases)

$$
\text{Area} = \frac{1}{2} \times (6 + 13) \times 3.30 = \frac{1}{2} \times 19 \times 3.30 = 9.5 \times 3.30 = 31.35
$$

✔ Answer: 31.35 square units

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6. Parallelogram

- Base = 11
- Height = 4 (the vertical side labeled 4 is the height)
- 5.27 is a slanted side — not needed

$$
\text{Area} = 11 \times 4 = 44
$$

✔ Answer: 44 square units

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✔ Final Answers:

| Problem | Shape | Area |
|--------|------------------|------------|
| 1 | Triangle | 36.75 |
| 2 | Parallelogram | 18 |
| 3 | Parallelogram | 10 |
| 4 | Trapezoid | 9.65 |
| 5 | Trapezoid | 31.35 |
| 6 | Parallelogram | 44 |

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📝 Notes:

- Always identify which side is the height (perpendicular to the base).
- For trapezoids, both parallel sides are bases.
- Slanted sides (like 5.63, 3.01, 5.27) are not used unless you’re calculating perimeter or using trigonometry — not needed here.

Let me know if you'd like this formatted as a printable answer sheet!